The timing of this share is crazy, since I was just looking around a few days ago to see if there were any guides or even kits for doing photolithography at home. It's part of my mission to demystify modern technology for my kids. I couldn't find anything, so this is excellent to see. Far too complex for my kids ages, but it might be cool to replicate at least part of this amazing project when they're older.
The Hacker Fab [1] project at Carnegie Mellon is creating and publishing guides to building simple fab equipment including photolithography and a sputtering system. For somewhat more complex equipment, I appreciate [2] from the founders of InchFab [3].
But maybe the easiest way to do (very low resolution) photolithography at home is to use dry film photoresist, which is like tape you can stick onto a copper PCB you then expose and etch; a cheap roll is ~$20 from eBay/Amazon.
Silk screen printing is probably the easiest way to introduce the concepts to kids. There are a lot of maker spaces/artist collectives and classes that have the basic tools and resources to do it.
It's not lithography, but you can build a working processor out of small surface mount chips, and you can solder these chips with lead-free solder. That seems very achievable for a motivated engineer, and probably involves much less toxic chemicals?
